59=0.5(x^2-3)

Solution for 59=0.5(x^2-3) equation:

59=0.5(x^2-3)

We move all terms to the left:

59-(0.5(x^2-3))=0


We calculate terms in parentheses: -(0.5(x^2-3)), so:

0.5(x^2-3)

We multiply parentheses

0.5x^2-1.5

Back to the equation:

-(0.5x^2-1.5)


We get rid of parentheses

-0.5x^2+1.5+59=0

We add all the numbers together, and all the variables

-0.5x^2+60.5=0

a = -0.5; b = 0; c = +60.5;
Δ = b2-4ac
Δ = 02-4·(-0.5)·60.5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-11}{2*-0.5}=\frac{-11}{-1}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+11}{2*-0.5}=\frac{11}{-1}
=-11
$